CAT Model Paper 3 Questions and Answers with Explanation Part 7

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Directions for question 35 to 37: Answer the questions based on the following data:

During the break of one week after the exams at SPAM (School of Private Administration and Management), the batch of 250 students decide to spend the entire week by watching movies. There are five movies that have been recently released, and every student watches at least one movie.

Further, at least three students watch any given combination of movie/movies. The movies released are Incidence, Where Is Little Lulu, Drop Out, To Hear Is Sin and Dead Immortals.

Q: 35. If every film is watched by students, at least how many students watch at most two movies?

(A)

(B)

(C)

(D) None of these

Ans: C

Solution

Let us first find out the number of combinations. We denote the number of instances by the number of tickets that have been bought.

It is given that for any combination on movie/movies there are at least three students who watch that movie/movies. Let us therefore find out the minimum number of students who will be present in each category. The same is given in the table below.

We see from the above table that there are at least 93 students who are buying 240 tickets. For the questions, let us treat them separately. It is given that each movie is watched by students, which means a total of tickets were sold. Out of these 600, we already know that tickets have been bought by students.

So the question is to now distribute the remaining tickets to remaining students, so that students watching exactly 1 or exactly 2 movies are the minimum.

We know, .

Since we have to minimize the number of students who watch exactly one or exactly two movies, let’s start by giving 3 tickets to each of the students, for which we need tickets. But there are only tickets. So, we have to take back tickets. Now if we take back 1 ticket from the students, students move from exactly 3 category to exactly 2 category, but if we take back tickets from each student, 55 students will move from exactly 3 to exactly 1 category. The remaining 1 ticket has to be taken back from the last student, and he moves to the exactly 2 category.

So minimum students are moving to the exactly or exactly category. Added to this would the already existing students from the earlier students. So total

Option (C).

Q: 36. What is the maximum number of students who can watch all five movies, given each movie is watched by 200 students?

(A)

(B)

(C)

(D)

Ans: B

Solution

Let us first find out the number of combinations. We denote the number of instances by the number of tickets that have been bought.

It is given that for any combination on movie/movies there are at least 3 students who watch that movie/movies. Let us therefore find out the minimum number of students who will be present in each category. The same is given in the table below.

We see from the above table that there are at least 93 students who are buying tickets. For the questions, let us treat them separately. Since each movie is watched by students, total number of tickets , out of which we already know that tickets have been bought by 93 students.

So we are left with tickets to be bought by students, so that maximum number of people buy 5 tickets.

Since , we can say that maximum students out of the can watch movies. But this also means that the remaining students are not watching any movie, which violates the condition given in the directions.

If we assume that students are watching 5 movies, which is just 1 less than , that accounts for tickets. Still, we are left with tickets to be distributed to 6 students such that each gets at least 1.

This is also not possible.

If we now say that students are watching 5 movies, this accounts for tickets, and we are left with tickets to be distributed to students such that each gets at least one.

This case is possible.

Hence from the students, maximum can watch all movies, and from the earlier students, are watching 5 movies.

Option B.

Q: 37. If each movie is watched by a different number of students, at most how many students can watch all 5 movies?

(A)

(B)

(C)

(D)

Ans: B

Solution

Let us first find out the number of combinations. We denote the number of instances by the number of tickets that have been bought.

It is given that for any combination on movie/movies there are at least 3 students who watch that movie/movies. Let us therefore find out the minimum number of students who will be present in each category. The same is given in the table below.

We see from the above table that there are at least 93 students who are buying 240 tickets. For the questions, let us treat them separately. There is no constraint on the number of tickets, and we have to maximize the number of students watching 5 movies.

Let us start by assuming that all 157 students watch 5 movies. But this would also mean that each movie is watched by the same number of people, as these 157 students contribute to the exactly 5 part, and the earlier 93 students are also symmetrically distributed.

Hence, let the 1st movie be watched by 7 students, 2nd movie by students, 3rd movie by students, 4th movie by students and the 5th movie by students.

To find the maximum number of students who watch all 5 movies, we have to take the minimum of the above values, which is .

Additionally, there are 3 students from the earlier students who are also watching 3 movies.

So total .

End Passage

Q: 38. The sentences, A, B, C, and D, below when properly sequenced, form a coherent paragraph. From among the four choices given below the question, choose the MOST LOGICAL ORDER of sentences that constructs a coherent paragraph.

(A) There is indeed strong evidence that the expansion of bank balance sheets (and private borrowing in general) helps drive economic growth

(B) Most bankers bristle when asked whether the finance industry is already big enough in relation to the rest of the economy.

(C) Initially growth in banking assets spurred economic growth, but soon a good chunk of it just inflated the size of the financial sector as banks created ever more securities to buy and sell from one another.

(D) Surprisingly, though, research indicates that once private borrowing gets close to of GDP it starts to slow down growth

(A) ADBC

(B) ABDC

(C) BADC

(D) BACD

Ans: C

Solution:

Sol: Here both A and B are decent starting sentences. A and D are connected. „There is …evidence‟ and „research indicates‟. Thus growth in banking assets while initially positive for economic growth later slows it down (AD). C explains why, at higher levels, banking assets fail to spur economic growth. Hence ADC is one unit. Now B may either B be the starting or ending sentence. From choices, BADC.

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